Abstract: A new fracture mechanics approach for in-situ stress determination by hydra-fracturing is proposed. It improves the fracture mechanics method as presented by Abou-Sayed etc. (1978). The accuracy of determination of the maximum horizontal stress (σHmax) is considerably enhanced by replacing fracture toughness of rock, K1c, and preexisting crack length L in rock by a new parameter U(U=K1c/√2) . The reason is that K1c is related to crack length L when crack length is smaller than a critical value and to determine the length of preexisting crack in rock as accurate as possible is very difficult. In addition the parameter U can be directly measured through a simple hollow-cylinder burst test. Based on recent experimental tests of fracture toughness of rock the new parameter U appears to be a constant when crack lengths are smaller than a certain critical value . The parameter √2 U may be taken also as a tensile strength of rock which contains small randomly distributed preexisting cracks.